Complex number proof (1 Viewer)

[Run hard@thehsc]

First two are easy, can someone help me out with the third one - not getting a start...

 

[jimmysmith560]

There appears to be an equivalent version of this question with additional parts. I will include both the questions and their respective working. Perhaps the additional parts can provide further guidance regarding how to approach part (iii):







I hope this helps!

 

[5uckerberg]

View attachment 34760
First two are easy, can someone help me out with the third one - not getting a start...

Is noting that and that for

Now diagramatically we will use the fact that is the complex conjugate of and as such .

With this is hand we know that a complex number plus its conjugate gives us two times the real part. Unfortunately we need to satisfy the fact that so therefore what you see here is the involvement of the so as such for the pattern there needs to be a to satisfy what we know from part i. Thus, after the dust is cleared

 

[Modern4DaBois]

@jimmysmith560 @5uckerberg how much time would you recommend spending on questions like these in tests?

 

[jimmysmith560]

@jimmysmith560 @5uckerberg how much time would you recommend spending on questions like these in tests?

Mark allocation is important in determining how long you should approximately spend on a particular question. For instance, one is less likely to spend a lot of time on a 1-2 mark question than a question with a mark allocation higher than 2 marks. It would also be a good idea not to spend too much time thinking about an approach to a particular question, i.e. if you cannot quickly think of a possible solution to a particular question, you should probably skip it and attempt other questions instead. Subsequently, you can come back to that question at a later point in the exam, once you have completed most other questions.